That's why I don't consider conversion efficiency and extraction efficiency to be synonyms. I follow the terminology used by BrewSmith and Brewers Friend.
Conversion efficiency equals the percentage of potential extract in the grain that is actually created in the mash.
Lauter efficiency equals the percentage of extract created in the mash that makes it into the boil kettle.
Mash efficiency equals the percentage of potential extract that makes it into the boil kettle. Mash efficiency = conversion efficiency * lauter efficiency.
Extract is the sugar, soluble proteins, (and all other dissolved material) that comes from the grain.
Based on the definition of the word extraction, "extraction efficiency" could plausibly be used to describe mash efficiency or lauter efficiency. So, I prefer not to use that term.
"First wort" sounds equivalent to the wort in the mash just prior to the start of lautering (unless you still have gradients at the start of lautering.) It is indeed possible to get 100% first wort efficiency, according to this definition, and it is equivalent to conversion efficiency.
Brew on